Monopoles and solitons have important topological aspects like quantized fl
uxes, winding numbers and curved target spaces. Naive discretizations which
substitute a lattice of points for the underlying manifolds are incapable
of retaining these features in a precise way. We study these problems of di
screte physics and matrix models and discuss mathematically coherent discre
tizations of monopolies and solitons using fuzzy physics and noncommutative
geometry. A fuzzy sigma-model action for the two-sphere fulfilling a fuzzy
Belavin-Polyakov bound is also put forth.